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2 years ago

How does drawing a rectangle support the idea of composing a larger unit from smaller units

Mathematics

1 answer:

pav-90 [236]2 years ago

4 0

Answer:

When you think rectangles, you think areas. Small areas aggregate to form bigger ones.

If you drew a rectangle, it's easy to divide it into smaller units by simply taking a line through its midsection from one length to the other and one width to the other. One can either form smaller squares or rectangles from a larger one.

When that is one, you'd have taken the larger area of a rectangle which is simply the product of the value of its length and it's the breadth, and divided it into smaller units.

Cheers!

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Suppose you know that the volume of the following prism is represent by V(x) = -2x^3 + 14x^2 + 120x.

erastova [34]

Step-by-step explanation:

-2x³ + 14x² + 120x

= -2x(x² - 7x - 60)

= -2x(x - 12)(x + 5).

The other 2 dimensions are -2x and (x + 5).

When using a graphing calculator to maximise the volume of the prism, we get x = 7.378. However this value is not reasonable as it makes -2x and (x - 12) negative, which are the sides of the prism.

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2 years ago

Krista's mom has told her she needs to make the pen ½ the size that she had planned (5 feet long by 4 ½ feet wide). What will th

saw5 [17]

Answer:

1. area of new pen = 11 $\frac{1}{4}$ $ft^{2}$

2. i. 5 feet by 2 $\frac{1}{4}$ feet

ii. 2 ½ feet by 4 ½ feet

Step-by-step explanation:

The size of the pen as planned = 5 ft long by 4 ½ ft wide

Area of the pen = length x width

= 5 x 4 ½

= 5 x $\frac{9}{2}$

Area of the pen = $\frac{45}{2}$

= 22 ½ $ft^{2}$

But, Krista has to make the pen ½ the size of planned. So that;

area of new pen = ½ x 22 ½

= ½ x $\frac{45}{2}$

= $\frac{45}{4}$

= 11 $\frac{1}{4}$

area of new pen = 11 $\frac{1}{4}$ $ft^{2}$

The area of the new pen would be 11 $\frac{1}{4}$ $ft^{2}$ .

The possible values she could use are:

i. 5 feet by 2 $\frac{1}{4}$ feet

ii. 2 ½ feet by 4 ½ feet

6 0

2 years ago

A college student Earned $6500 during summer vacation working as a waiter. The student invested Part of the money at 10% and the

Juliette [100K]

Answer:

The amount invested at 10% rate is $ 2200

Step-by-step explanation:

Given as :

The total amount earn by student = $6500

The total interest received at the end of year = $607

Let the amount invested at 10% rate = $x

So, The amount invested at 9% rate = ($6500 - $x)

Let the time for which money invested = 1 year

<u>Now from Simple Interest method :</u>

SI = $\frac{principal\times Rate\times Time}{100}$

Or, SI_1 + SI_2 = $\frac{x\times 10\times 1}{100}$ + $\frac{(6500-x)l\times 9\times 1}{100}$

Or, SI_1 + SI_2 = $(\frac{10x}{100})+\frac{(6500-x)\times 9}{100}$

Or, $607 × 100 = 10x + (6500-x) × 9

Or, $60700 = 10x- 9x + 58500

Or, $60700 - $58500 = x

Or , 2200 = x

∴ x = 2200

So, The amount invested at 10% rate = $x = $ 2200

Hence The amount invested at 10% rate is $ 2200 Answer

5 0

2 years ago

Sarah saved $12.75 every week for a number of weeks, w. She received an additional $25 during the last week in which she saved m

Umnica [9.8K]

Answer:

12.75w + 25 = 114.25

w = 7

Step-by-step explanation:

since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet) we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.

to find out what w represents, we have to solve for it. solving for w means isolating it on one side. so, what we can do first is subtract 25 from both sides. that would then make the equation:

12.75w = 89.25

now, we have only one step left to isolating w, and that's to get 12.75 on the other side somehow. since we're multiplying 12.75 with w, and we're applying additive inverse properties, meaning the opposite of what is happening to cancel it out on the side it's in, we would divide 12.75 on both sides. in the left, 12.75 would cancel out, and in the right, we would divide 89.25 by 12.75. the quotient is 7.

now there's nothing left to take out to isolate w, so we have:

w = 7

sarah saved up for 7 weeks.

3 0

2 years ago

I need the work to please

Free_Kalibri [48]

There you go I hope it helps

7 0

2 years ago

Read 2 more answers